***

rsType <- c("observed", "rarefied", "msom")[2]
rSMet_base <- c("observed"="propStrata", "rarefied"="range_size_samp", "msom"="range_size_mu")[rsType]
rSMet_annComm <- c("observed"="propStrata_avg", "rarefied"="range_size_samp_avg", "msom"="range_size_mu_avg")[rsType]
rSMet_ltComm <- c("observed"="propStrata_avg_ltAvg", "rarefied"="range_size_samp_avg_ltAvg", "msom"="range_size_mu_avg_ltAvg")[rsType]

rR <-  c("observed"="naive_rich", "rarefied"=NA, "msom"="reg_rich")[3]
lR <-  c("observed"="local_rich_obs", "rarefied"="local_rich_samp", "msom"="local_rich")[2]
betaD <-  c("observed"="beta_div_obs", "msom"="beta_div_mu")[1]

There are four primary metrics:
- range size
- regional richness (gamma)
- local richness (alpha)
- spatial beta diversity

Each of these metrics can be based on raw observations or on MSOM estimates, and some can also be based on a rarefied (resampled, or ‘samp’) set of observations.

Furthermore, the range size metric can be based on a few combinations of cross-year and/or cross-species averages. The base metric for range size (no averaging) is used to to examine how range size changes with time until extinction and time after colonization. A cross-species average of a given year’s observed range sizes (_avg) is used for the rare species to see how this sub-group changes in its geographic distribution, or when making specialized comparisons. A cross-year average (ltAvg) is used to relate a species’ ‘typical’ range size to the total number of colonizations and extinctions it experienced during the time series. A cross-year (all years a species was observed) followed by a cross-species (species present in a given year) average (_avg_ltAvg) is used to compare species richness to the typical range size of species in the community.

# ============
# = Richness =
# ============

Basic Info

Number of Speices

Number of species across all regions: 581

Species Richness

Table. Summary of richness mean and variability

Long-term mean and standard deviation in MSOM richness, and average of those sd’s. Gmex and Shelf have the highest and lowest long-term averages in species richness (MSOM).
reg mu sd mu_sd
ai 52.499 2.3143 5.299
ebs 103.611 5.5665 5.299
gmex 142.285 4.2663 5.299
goa 95.717 8.5061 5.299
neus 122.030 8.2371 5.299
newf 65.761 4.3653 5.299
sa 102.435 4.0355 5.299
shelf 46.300 3.2469 5.299
wctri 84.478 7.1532 5.299

Figure 1. MSOM richness time series

# load regression results
load("../../pkgBuild/results/rich_naive_trend_kendall.RData")
rich_naive_trend_kendall[reg!="wcann",BH:=p.adjust(taup, method='BH')]
rich_naive_trend_kendall <- rich_naive_trend_kendall[
    reg!="wcann",list(reg=reg, estimate=tau, BH=BH, pvalue=taup)
]
load("../../pkgBuild/results/rich_trend_kendall.RData")
rich_trend_kendall[reg!="wcann",BH:=p.adjust(pvalue, method="BH")]
rich_trend_kendall <- rich_trend_kendall[
    reg!="wcann",list(reg=reg, estimate=tau, BH=BH, pvalue=pvalue)
]

# make plot
load("../results/rich_trend_kendall.RData") # load rich trend stats
richness_ts()
pdf("../../submitted_pdfs/final/Fig1.pdf", width=3.228, height=4.6114)
richness_ts()
dev.off()
quartz_off_screen 2
**Figure 1.** Time series of MSOM estimates of region richness. Each point is the posterior mean of regional richness in a year. Lines indicate long-term trends from fitted values of linear regression models predicting richness from time.

Figure 1. Time series of MSOM estimates of region richness. Each point is the posterior mean of regional richness in a year. Lines indicate long-term trends from fitted values of linear regression models predicting richness from time.

Looking for trends in species richness in both the naive estimates and the MSOM estimates. Using Kendall’s Tau_b, calculated for 1E4 resamplings of the posterior of richness. Tau is also calculated using a method that removes serial correlation to achieve independence of observations so that the p-values are correct.

In the Naive estimates, 7 regions had significant \(\tau_b\).

Table 1. MSOM tau

Table 2. MSOM richness trends in each region. Estimate is Kendall’s Tau_b, BH is the Benjamini-Hochberg corrected p-value, and p.value is the original p-value. Trends are calculated for 1E4 resampled combinations of the richness posterior. For each resampling, independence of observations is achieved before estimating Tau by removing serial correlation from resampled time series. This procedure retains the integrity of p-values.
reg tau Z pvalue
ebs 0.42141 3.31119 0.00093
ai 0.08918 0.37542 0.70735
goa 0.24549 1.08760 0.27677
wctri 0.60763 2.34639 0.01896
wcann 0.41618 1.67804 0.09334
gmex 0.09637 0.51845 0.60414
sa -0.21815 -1.47174 0.14109
neus 0.19111 1.50292 0.13286
shelf 0.45244 4.06179 0.00005
newf 0.72656 3.80999 0.00014

In the MSOM estimates, 4 regions had significant \(\tau_{b}\).

Overall, ~half the regions show positive trends. No regions show significant negative trends (although SEUS is close, depending on the analysis). It’s a bit surprising how much removing the autocorrelation seemed to impact some of the trends (AI in particular, I think).

Manuscript paragraph:
Estimated slopes for long-term trends (Kendall’s \(\tau_b\)) in richness were positive for most regions. For Naive estimates, all the seven positive \(\tau\) were also significantly different from 0, whereas the two negative \(\tau_b\), Aleutian Islands and Southeast US, were not (Table S2). Long-term trends in MSOM estimates of richness had the same sign as Naive trends, except for Aleutian Islands, but now the only significant \(\tau_b\) were the following four regions: Eastern Bering Sea (\(\tau_b\) = 0.42141), West Coast US (\(\tau_b\) = 0.60763), Scotian Shelf (\(\tau_b\) = 0.45244 ), and Newfoundland (\(\tau_b\) = 0.72656 ) (Table 1). Richness trends were not significant in the Gulf of Mexico, Gulf of Alaska, and Northeast US, Aleutian Islands, Southeast US.

Colonization and Extinction

Colonization and Extinction Summary

The number of species-regions: 863
The number of core species: 536
The number of both species: 263
The number of colonizing species: 60
The number of leaving species: 4

Richness and Range Size

Do Transient Species Have Smaller Ranges than Core Species?

transRange <- spp_master[,list(reg=reg, spp=spp, transient=(ce_categ!='neither'),rangeSize=range_size_samp)]
ur <- names(pretty_reg)
nr <- length(ur)
tR_mod <- structure(vector('list', length(ur)), .Names=ur)
for(r in 1:nr){
    tR_mod[[ur[r]]] <- lmer(rangeSize~transient + (1|spp), data=transRange[reg==ur[r]])
}
tR_mod_smry <- smry_modList2(tR_mod)
kable(tR_mod_smry)
reg mod_call MargR2 CondR2 AIC pval_transient BH_transient randGrp Int transientTRUE
ai rangeSize~transient+(1|spp) 0.07447 0.8741 -1233.9 0.02037 0.020 spp 0.25240 -0.13085
ebs rangeSize~transient+(1|spp) 0.16380 0.9404 -8293.1 0.00000 0.000 spp 0.27140 -0.19520
gmex rangeSize~transient+(1|spp) 0.11860 0.8461 -5264.1 0.00000 0.000 spp 0.19516 -0.14126
goa rangeSize~transient+(1|spp) 0.10370 0.9322 -3308.5 0.00030 0.000 spp 0.17728 -0.12959
neus rangeSize~transient+(1|spp) 0.41200 0.8827 -11018.4 0.00000 0.000 spp 0.19523 -0.17705
newf rangeSize~transient+(1|spp) 0.08736 0.9014 -2573.9 0.00214 0.002 spp 0.18857 -0.12827
sa rangeSize~transient+(1|spp) 0.28070 0.8110 -3536.0 0.00000 0.000 spp 0.34518 -0.28582
shelf rangeSize~transient+(1|spp) 0.30740 0.8681 -4145.8 0.00000 0.000 spp 0.28011 -0.22187
wctri rangeSize~transient+(1|spp) 0.11340 0.8470 -1328.3 0.00004 0.000 spp 0.24779 -0.17944 
transDiffMean <- tR_mod_smry[,mean(transientTRUE)]*100
sign_tDM <- sign(transDiffMean)

In mixed effects models with intecepts varying among species and transient versus core as a categorical predictor, transient species had range sizes that were 17.65964 (% occupancy) smaller than the ranges of core species (average intercept adjustment; all \(p \leq\) 0.02 after correcting for multiple tests).

Richness and Geographic Range

Figure 3. Richness versus Community Range Index

rich_geoRange(rSMet_ltComm, leg=TRUE, legPan=1, panLab=FALSE)
pdf("../../submitted_pdfs/final/Fig3.pdf", width=3.228, height=3.228)
rich_geoRange(rSMet_ltComm, leg=TRUE, legPan=1, panLab=FALSE)
dev.off()
quartz_off_screen 2
**Figure 3.** Species richness vs geographic range size. Range size is presented as each species' long-term average of the proportion of sites it occupied. Solid lines are linear regressions with MSOM richness as the response and the horizontal axis and an intercept as the predictors.

Figure 3. Species richness vs geographic range size. Range size is presented as each species’ long-term average of the proportion of sites it occupied. Solid lines are linear regressions with MSOM richness as the response and the horizontal axis and an intercept as the predictors.

Range size is a pretty good predictor of species richness. I think I had originally missed the range size relationship b/c I hadn’t done the same aggregating procedure. The interpretation I have is that richness is highest when you have a bunch of rare species.

Regressions relating Richness to Community Range Index

range_reg <- make_range_reg(dens="propTow_occ_avg", size=rSMet_ltComm)

# Fit different models to the whole data set
# Models vary in which/ how parameters vary among regions
rSize_mods <- list()
rSize_mods[[1]] <- lm(rich ~ size, data=range_reg) # simple
rSize_mods[[2]] <- lm(rich ~ size*reg, data=range_reg) # slope and intercept ind. among regs
rSize_mods[[3]] <- lme4::lmer(rich ~ size + (1|reg), data=range_reg) # intercept varies randomly among regs
rSize_mods[[4]] <- lme4::lmer(rich ~ size + (size|reg), data=range_reg) # slope & int. vary randomly among regs
rich_size_smry <- smry_modList(rSize_mods) # summarize to get R^2, AIC, p-vals, etc
## Note: method with signature 'sparseMatrix#ANY' chosen for function 'kronecker',
##  target signature 'dgCMatrix#ngCMatrix'.
##  "ANY#sparseMatrix" would also be valid
# Fit simple model to each region separately 
ur <- range_reg[,unique(reg)]
rSize_reg_mods <- structure(vector("list",length(ur)), .Names=ur)
for(r in 1:length(ur)){
    rSize_reg_mods[[r]] <- lm(rich ~ size, data=range_reg[reg==ur[r]])
}
rich_s_reg_smry <- data.table(reg=ur, smry_modList(rSize_reg_mods)) # summarize
setnames(rich_s_reg_smry, old=c("Marginal","Conditional","p.value"), new=c("MargR2","CondR2","pval")) # rename
setkey(rich_s_reg_smry, reg, Class, mod_call, predictor) # sort
rich_s_reg_smry[, BH:=round(p.adjust(pval, "BH"), 3), by=c("mod_call", "predictor")] # correct p-vals for multiple tests
smry_formula <- formula(reg+Class+mod_call+MargR2+CondR2+AIC~predictor) # formula to organize
rich_s_reg_smry <- dcast(rich_s_reg_smry, smry_formula, value.var=c("pval", "BH")) # organize; helpful if multiple predictors
Regression models of richness predicted by community metric of range size, but each region has a separate model.
reg Class mod_call MargR2 CondR2 AIC pval_size BH_size
ai lm rich ~ size 0.7348 NA 43.222 0.0004 0.000
ebs lm rich ~ size 0.8696 NA 136.247 0.0000 0.000
gmex lm rich ~ size 0.7684 NA 77.674 0.0000 0.000
goa lm rich ~ size 0.7908 NA 77.173 0.0000 0.000
neus lm rich ~ size 0.8609 NA 167.633 0.0000 0.000
newf lm rich ~ size 0.9151 NA 58.069 0.0000 0.000
sa lm rich ~ size 0.3582 NA 134.595 0.0016 0.002
shelf lm rich ~ size 0.8999 NA 123.548 0.0000 0.000
wctri lm rich ~ size 0.9510 NA 42.516 0.0000 0.000
Average of above region-specific rich ~ size models.
mod_call reg Class MargR2 CondR2 AIC pval_size BH_size
rich ~ size NA NA 0.7943 NA 95.631 0.00022 0.00022

Manuscript Text:
Furthermore, species richness was negatively correlated with the community range index (CRI) in each region (Fig. 3; separate linear regression for each region, for slope all corrected \(p \leq\) 0.002, \(0.3582 \leq R^2 \leq 0.951\), average \(R^2 = 0.7943\) ).

**Other Notes:**
All models are pretty good predictors. Well, the most basic model kinda sucks I guess. It needs to account for some of the between-region variation.

Predicting Richness: Range Size or Density? As far as picking one or the other, it doesn’t end up mattering much. Range size is a lot better than density in NEUS, and density outperforms size in AI. Otherwise, size as a slight edge over density on average, although both predictors are significant in all regions.

Conclusion for Richness and Geographic Range The two metrics of geographic range are well correlated. Furthermore, richness can be predicted pretty well using regressions with either as a predictor. There are large differences among regions, though. This is probably because richness is not readily comparable among most regions. Regions vary mostly in their intercept values, and they have fairly similar slopes (though they are not identical, and model fits improve when allowing slopes to vary among regions; it’s just that the improvement is small compared to allowing intercepts to vary among regions).

The interpretation of the result that geographic distribution predicts species richness is likely associated with species rarity. When the average range density or range size of a community is low, it means it has a lot of species that are rare (at either spatial scale). It’s these rare species that come and go, and form the dynamics of richness that we observe. When that dynamical value is high, it implies that an above-average number of the dynamic species are present. Because those species are transient (dynamic), they are also probably rare.

Range Size Over Time For Core & Transients

Figure 4. Range size over time for transient & core

eval(neitherPres_subColor())
plot_rangeSize_FullTrans(range_type="range_size_samp")
pdf("../../submitted_pdfs/final/Fig4.pdf", width=6.81102, height=6.81102)
plot_rangeSize_FullTrans(range_type="range_size_samp")
dev.off()

quartz_off_screen 2

Range Size over time for transient & core – Stats

transMod <- structure(vector("list",length(ur)), .Names=ur)
coreMod <- structure(vector("list",length(ur)), .Names=ur)
ctMod <- structure(vector("list",length(ur)), .Names=ur)
ctMod2 <- ctMod
for(r in 1:length(ur)){
    rr <- ur[r]
    td <- spp_master[eval(rE_logic1)]
    td[,year:=year-min(year)]
    transMod[[r]] <- lmer(range_size_samp~year+(1|spp), data=td)
    
    td2 <- spp_master[eval(rE_logic3)]
    td2[,year:=year-min(year)]
    coreMod[[r]] <- lmer(range_size_samp~year+(1|spp), data=td2)
    
    td3 <- spp_master[reg==rr & present==1]
    td3[,year:=year-min(year)]
    td3[,categ2:=c("core","transient")[(ce_categ!="neither")+1L]]
    ctMod[[r]] <- lmer(range_size_samp~year*categ2+(1|spp), data=td3)
    
    ctMod2[[r]] <- lm(range_size_samp~year*categ2, data=td3)
    # ctMod2[[r]] <- lmer(range_size_samp~year+(year|spp), data=td)
    # ctMod2[[r]] <- lmer(range_size_samp~year+(year|spp), data=td3)
    # ctMod2[[r]] <- lmer(range_size_samp~year*categ2+(year|spp), data=td3)
    # td3[,auto.arima(range_size_samp, xreg=as.matrix(cbind(year=year, categ2=(categ2=="transient"), year_categ2=(year*(categ2=="transient")))), allowdrift=FALSE, d=0)]

}
transExpansionStats <- smry_modList2(transMod)
coreExpansionStats <- smry_modList2(coreMod)
ctExpansionStats <- smry_modList2(ctMod)
# ctExpansionStats2 <- smry_modList2(ctMod2)

meanNum <- function(x, ...){
    if(storage.mode(x) %in% c("double", "integer", "logical")){
        mean(x, ...)
    }else{
        NA
    }
}

kable(rbind(transExpansionStats,lapply(transExpansionStats, meanNum), transExpansionStats[BH_year<0.05, lapply(.SD, meanNum)][,reg:="signifYear"]))
reg mod_call MargR2 CondR2 AIC pval_year BH_year randGrp Int year
ai range_size_samp~year+(1|spp) 0.04978 0.63660 -266.83 1e-05 0 spp 0.05853 0.00343
ebs range_size_samp~year+(1|spp) 0.01409 0.82480 -3383.90 0e+00 0 spp 0.05250 0.00143
gmex range_size_samp~year+(1|spp) 0.03786 0.63360 -1543.33 0e+00 0 spp 0.02259 0.00363
goa range_size_samp~year+(1|spp) 0.07234 0.57180 -1322.23 0e+00 0 spp 0.01342 0.00186
neus range_size_samp~year+(1|spp) 0.02210 0.54520 -8917.73 0e+00 0 spp 0.01091 0.00044
newf range_size_samp~year+(1|spp) 0.03951 0.66150 -719.18 0e+00 0 spp 0.03018 0.00315
sa range_size_samp~year+(1|spp) 0.05840 0.34100 -1760.63 0e+00 0 spp 0.08827 -0.00252
shelf range_size_samp~year+(1|spp) 0.12960 0.56570 -2508.97 0e+00 0 spp 0.01941 0.00170
wctri range_size_samp~year+(1|spp) 0.11650 0.45570 -332.63 0e+00 0 spp -0.01374 0.00488
NA NA 0.06002 0.58177 -2306.16 0e+00 0 NA 0.03134 0.00200
signifYear NA 0.06002 0.58177 -2306.16 0e+00 0 NA 0.03134 0.00200 
kable(rbind(coreExpansionStats,lapply(coreExpansionStats, meanNum), coreExpansionStats[BH_year<0.05, lapply(.SD, meanNum)][,reg:="signifYear"]))
reg mod_call MargR2 CondR2 AIC pval_year BH_year randGrp Int year
ai range_size_samp~year+(1|spp) 0.00004 0.90040 -969.63 0.65562 0.65600 spp 0.24991 0.00015
ebs range_size_samp~year+(1|spp) 0.00289 0.94840 -5170.31 0.00000 0.00000 spp 0.24800 0.00156
gmex range_size_samp~year+(1|spp) 0.00047 0.84690 -3827.05 0.01919 0.02500 spp 0.18865 0.00081
goa range_size_samp~year+(1|spp) 0.00084 0.94090 -2142.47 0.00063 0.00100 spp 0.16622 0.00070
neus range_size_samp~year+(1|spp) 0.01428 0.85840 -4630.15 0.00000 0.00000 spp 0.16285 0.00209
newf range_size_samp~year+(1|spp) 0.00150 0.91320 -1913.24 0.00024 0.00000 spp 0.20137 -0.00171
sa range_size_samp~year+(1|spp) 0.00268 0.77120 -2162.97 0.00001 0.00000 spp 0.36634 -0.00176
shelf range_size_samp~year+(1|spp) 0.00041 0.83910 -2177.36 0.09164 0.10300 spp 0.28729 -0.00036
wctri range_size_samp~year+(1|spp) 0.02543 0.89720 -1165.98 0.00000 0.00000 spp 0.18834 0.00440
NA NA 0.00540 0.87952 -2684.35 0.08526 0.08722 NA 0.22878 0.00065
signifYear NA 0.00687 0.88231 -3001.74 0.00287 0.00371 NA 0.21740 0.00087 
kable(rbind(ctExpansionStats,lapply(ctExpansionStats, meanNum), ctExpansionStats[BH_year<0.05, lapply(.SD, meanNum)][,reg:="signifYear"], ctExpansionStats[`BH_year:categ2`<0.05, lapply(.SD, meanNum)][,reg:="signifYear:categ2"]))
reg mod_call MargR2 CondR2 AIC pval_categ2 pval_year pval_year:categ2 BH_categ2 BH_year BH_year:categ2 randGrp Int year categ2transient year:categ2transient
ai range_size_samp~year*categ2+(1|spp) 0.07939 0.87930 -1227.8 0.01933 0.00886 0.00002 0.01900 0.01000 0.00000 spp 0.24991 0.00015 -0.19203 0.00330
ebs range_size_samp~year*categ2+(1|spp) 0.16860 0.94380 -8437.4 0.00000 0.00000 0.56113 0.00000 0.00000 0.59200 spp 0.24800 0.00156 -0.19537 -0.00014
gmex range_size_samp~year*categ2+(1|spp) 0.12140 0.84870 -5271.7 0.00000 0.00000 0.00008 0.00000 0.00000 0.00000 spp 0.18865 0.00081 -0.16610 0.00282
goa range_size_samp~year*categ2+(1|spp) 0.10660 0.93470 -3318.8 0.00023 0.00000 0.00259 0.00000 0.00000 0.00400 spp 0.16622 0.00070 -0.15278 0.00116
neus range_size_samp~year*categ2+(1|spp) 0.42250 0.89330 -11307.9 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 spp 0.16285 0.00209 -0.15195 -0.00165
newf range_size_samp~year*categ2+(1|spp) 0.09326 0.90410 -2570.9 0.00239 0.04512 0.00000 0.00300 0.04500 0.00000 spp 0.20137 -0.00171 -0.17034 0.00481
sa range_size_samp~year*categ2+(1|spp) 0.28460 0.81490 -3550.6 0.00000 0.00000 0.22953 0.00000 0.00000 0.29500 spp 0.36634 -0.00176 -0.27804 -0.00079
shelf range_size_samp~year*categ2+(1|spp) 0.31270 0.87250 -4165.8 0.00000 0.00903 0.00000 0.00000 0.01000 0.00000 spp 0.28729 -0.00036 -0.26814 0.00207
wctri range_size_samp~year*categ2+(1|spp) 0.14520 0.87880 -1468.3 0.00001 0.00000 0.59204 0.00000 0.00000 0.59200 spp 0.18834 0.00440 -0.20238 0.00047
NA NA 0.19269 0.88557 -4591.0 0.00244 0.00700 0.15393 0.00244 0.00722 0.16478 NA 0.22878 0.00065 -0.19746 0.00134
signifYear NA 0.19269 0.88557 -4591.0 0.00244 0.00700 0.15393 0.00244 0.00722 0.16478 NA 0.22878 0.00065 -0.19746 0.00134
signifYear:categ2 NA 0.18931 0.88877 -4643.8 0.00366 0.01050 0.00045 0.00367 0.01083 0.00067 NA 0.20938 0.00028 -0.18356 0.00209

Range Size over time for transient vs core – Text

Examining how range size changed over time for “core” and “transient” groups of species. Core species are those that are present in all years. Transient species are those that are not present in all years. 9 regions had significant trends in range size for transient species (average slope for regions with significant trend = 0.002), and 7 regions had significant trends in range size for core species (ai, shelf did not have significant trends for core species; averge slope for regions with significant trend = 8.7071910^{-4}).

Given that many regions showed positive trends in range size for both species groups, it is prudent to compare trends between these groups, to see if they differ. To this end, I analyzed the groups together, and tested the significance of an interaction term that adjusted the a baseline slope if the species was in the transient group.

Note that transient species are very much expected to have a smaller range size than the core group, particularly at the beginning of the time series; I’m not dynamically reporting the significance of the difference in intercepts here, but at the time of writing all regions showed significant differences in intercept between groups, with the transient group having a smaller intercept than the core group.

Interestingly, 9 regions had significant trends (main effect), and newf, sa, shelf had significant negative trends, while ai, ebs, gmex, goa, neus, wctri had significant positive trends. ebs, sa, wctri were the regions without significant interactions – (at the time of this writing) these are not the same regions that lacked significant trends in the core group. If we sum the main effect and transient-interaction together (ignoring significance), we see that sa was/were the only region/s with negative estimated trends for transient species; all others had positive trends in range for transients. Some regions had significant trends for both core and transients, but the direction of these trends differed between the two groups: newf, shelf had core species with trends in range size that were significantly less than 0 but transient species with trends in range size that were significantly greater than 0.

Southeast U.S. core species long-term slope \(\beta_Y=\)-1.76278 (percent per decade)
Newfoundland core species slope \(\beta_Y=\)-1.7062 (percent per decade)
Scotian Shelf core species slope \(\beta_Y=\)-0.35899 (percent per decade)

For core species with positive long-term slopes, the average was **${}_{Y+}=\(1.61859** (percent per decade). After correcting for multipel testing, all **\)p $ 0.045**

However, the interaction term indicated that the slopes of core and transient species were different in 6 of the regions (\(p \leq\) 0.004), including positive interactions in Newfoundland (\(\beta_{Y \times T} =\) 4.81063) and Scotian Shelf (\(\beta_{Y \times T} =\) 2.0651). Excluding the Southeast U.S., the average long-term trend in range size for transient species was 2.56144

Supplement

Figure S1. Map of Site Locations

plotSiteMap()

List of Species sampled

spp_master[,j={cat('\n\n\n\n\n');cat('**',reg[1],'**',sep=''); cat('\n\n'); cat(paste(sort(unique(spp)),collapse=', '));cat('\n');NULL},by='reg']

ai

Anoplopoma fimbria, Aptocyclus ventricosus, Atheresthes evermanni, Atheresthes stomias, Bathymaster signatus, Bathyraja aleutica, Bathyraja maculata, Bathyraja parmifera, Bathyraja taranetzi, Berryteuthis magister, Careproctus rastrinus, Cheiraster dawsoni, Chionoecetes bairdi, Chlamys rubida, Dasycottus setiger, Enteroctopus dofleini, Erimacrus isenbeckii, Eumicrotremus orbis, Fusitriton oregonensis, Gadus macrocephalus, Glyptocephalus zachirus, Gorgonocephalus eucnemis, Gymnocanthus galeatus, Hemilepidotus jordani, Hemilepidotus zapus, Hemitripterus bolini, Hippoglossoides elassodon, Hippoglossus stenolepis, Hyas lyratus, Lethotremus muticus, Lithodes aequispinus, Malacocottus zonurus, Microstomus pacificus, Modiolus modiolus, Myoxocephalus polyacanthocephalus, Oregonia gracilis, Pagurus aleuticus, Pandalus eous, Pandalus tridens, Pleurogrammus monopterygius, Podothecus accipenserinus, Reinhardtius hippoglossoides, Rossia pacifica, Sarritor frenatus, Sebastes alutus, Sebastes borealis, Sebastes polyspinis, Sebastolobus alascanus, Strongylocentrotus droebachiensis, Theragra chalcogramma, Triglops forficatus, Triglops macellus, Triglops scepticus, Zaprora silenus

ebs

Aforia circinata, Ammodytes hexapterus, Argis dentata, Argis lar, Artediellus pacificus, Asterias amurensis, Atheresthes stomias, Bathymaster signatus, Beringius behringi, Boltenia ovifera, Buccinum angulosum, Buccinum plectrum, Buccinum polare, Buccinum scalariforme, Chionoecetes bairdi, Chionoecetes opilio, Chrysaora melanaster, Ciliatocardium ciliatum, Clinopegma magnum, Clupea pallasii pallasii, Crangon dalli, Crossaster papposus, Cucumaria fallax, Cyanea capillata, Dasycottus setiger, Echinarachnius parma, Eleginus gracilis, Erimacrus isenbeckii, Eunoe depressa, Eunoe nodosa, Euspira pallida, Evasterias echinosoma, Fusitriton oregonensis, Gadus macrocephalus, Gersemia rubiformis, Glebocarcinus oregonensis, Glyptocephalus zachirus, Gorgonocephalus eucnemis, Grandicrepidula grandis, Halichondria panicea, Halocynthia aurantium, Hemilepidotus jordani, Hemitripterus bolini, Hexagrammos stelleri, Hiatella arctica, Hippoglossoides elassodon, Hippoglossoides robustus, Hippoglossus stenolepis, Hyas coarctatus, Hyas lyratus, Icelus spatula, Icelus spiniger, Leptasterias arctica, Leptasterias groenlandica, Leptasterias polaris, Leptoclinus maculatus, Lethasterias nanimensis, Limanda aspera, Limanda proboscidea, Limanda sakhalinensis, Liparis gibbus, Liponema brevicorne, Lycodes brevipes, Lycodes palearis, Lycodes raridens, Mactromeris polynyma, Mallotus villosus, Metridium farcimen, Musculus discors, Neocrangon communis, Neptunea borealis, Neptunea heros, Neptunea lyrata, Neptunea pribiloffensis, Neptunea ventricosa, Occella dodecaedron, Ophiura sarsii, Oregonia gracilis, Pandalus eous, Pandalus goniurus, Paralithodes camtschaticus, Paralithodes platypus, Patinopecten caurinus, Platichthys stellatus, Pleuronectes quadrituberculatus, Plicifusus kroeyeri, Podothecus accipenserinus, Pteraster obscurus, Pyrulofusus deformis, Pyrulofusus melonis, Reinhardtius hippoglossoides, Rhamphostomella costata, Sarritor frenatus, Serratiflustra serrulata, Serripes groenlandicus, Siliqua alta, Stomphia coccinea, Strongylocentrotus droebachiensis, Styela rustica, Tellina lutea, Telmessus cheiragonus, Thaleichthys pacificus, Theragra chalcogramma, Trichodon trichodon, Triglops pingelii, Triglops scepticus, Tritonia diomedea, Urticina crassicornis, Volutopsius fragilis, Volutopsius middendorffii

gmex

Achelous spinicarpus, Achelous spinimanus, Amusium papyraceum, Anadara baughmani, Anasimus latus, Anchoa hepsetus, Anchoa lyolepis, Anchoa mitchilli, Anchoviella perfasciata, Ancylopsetta dilecta, Ancylopsetta ommata, Arenaeus cribrarius, Ariopsis felis, Balistes capriscus, Bellator militaris, Bollmannia communis, Bregmaceros atlanticus, Brevoortia patronus, Brotula barbata, Calappa sulcata, Callinectes sapidus, Callinectes similis, Caranx crysos, Caulolatilus intermedius, Centropristis philadelphica, Chaetodipterus faber, Chloroscombrus chrysurus, Chrysaora quinquecirrha, Citharichthys macrops, Citharichthys spilopterus, Cyclopsetta chittendeni, Cynoscion arenarius, Cynoscion nothus, Decapterus punctatus, Diplectrum bivittatum, Diplectrum formosum, Doryteuthis pleii, Engraulis eurystole, Engyophrys senta, Etropus crossotus, Etropus microstomus, Etrumeus teres(sadina), Eucinostomus gula, Farfantepenaeus aztecus, Farfantepenaeus duorarum, Fowlerichthys radiosus, Gymnachirus texae, Gymothorax igromargiatus, Haemulon aurolineatum, Halieutichthys aculeatus, Harengula jaguana, Hepatus epheliticus, Hoplunnis macrurus, Kathetostoma albigutta, Lagocephalus laevigatus, Lagodon rhomboides, Larimus fasciatus, Leiostomus xanthurus, Lepophidium brevibarbe, Lepophidium jeannae, Libinia dubia, Libinia emarginata, Litopenaeus setiferus, Loligo pealeii, Lolliguncula brevis, Lutjanus campechanus, Lutjanus synagris, Menticirrhus americanus, Micropogonias undulatus, Mullus auratus, Mustelus canis, Neobythites gilli, Neomerinthe hemingwayi, Ophidion holbrookii, Ophidion welshi, Opisthonema oglinum, Orthopristis chrysoptera, Ovalipes floridaus, Ovalipes stephensoni, Paralichthys lethostigma, Parapenaeus politus, Pareques umbrosus, Parthenopoides massena, Peprilus burti, Peprilus paru, Pericoptus punctatus, Peristedion gracile, Polydactylus octoemus, Pontinus longispinis, Porichthys plectrodon, Portunus gibbesii, Priacanthus arenatus, Prionotus longispinosus, Prionotus ophryas, Prionotus roseus, Prionotus rubio, Prionotus scitulus, Prionotus stearnsi, Prionotus tribulus, Pristipomoides aquilonaris, Raioides louisiaesis, Raja texana, Rhizoprionodon terraenovae, Rhomboplites aurorubens, Rhynchoconger flavus, Rimapenaeus constrictus, Rimapenaeus similis, Sardinella aurita, Saurida brasiliensis, Saurida caribbaea, Scomber japonicus, Scomberomorus cavalla, Scomberomorus maculatus, Scorpaena calcarata, Selar crumenophthalmus, Selene setapinnis, Seriola dumerili, Serranus atrobranchus, Sicyonia brevirostris, Sicyonia burkenroadi, Sicyonia dorsalis, Soleocera vioscai, Sphoeroides parvus, Sphyraena guachancho, Squatina dumeril, Squilla chydaea, Squilla empusa, Steindachneria argentea, Stellifer lanceolatus, Stenotomus caprinus, Stephanolepis hispidus, Syacium gunteri, Syacium papillosum, Symphurus civitatum, Symphurus diomedeanus, Symphurus plagiusa, Synodus foetens, Synodus poeyi, Trachurus lathami, Trichiurus lepturus, Trichopsetta ventralis, Upeneus parvus, Urophycis cirrata, Urophycis floridana

goa

Albatrossia pectoralis, Anoplopoma fimbria, Aphrocallistes vastus, Aptocyclus ventricosus, Arctomelon stearnsii, Atheresthes stomias, Bathymaster signatus, Bathyraja aleutica, Bathyraja interrupta, Bathyraja parmifera, Berryteuthis magister, Brisaster latifrons, Chionoecetes bairdi, Chlamys rubida, Clupea pallasii pallasii, Ctenodiscus crispatus, Cucumaria fallax, Cyanea capillata, Dasycottus setiger, Doris odhneri, Enteroctopus dofleini, Eumicrotremus orbis, Eumicrotremus phrynoides, Fusitriton oregonensis, Gadus macrocephalus, Glebocarcinus oregonensis, Glyptocephalus zachirus, Gorgonocephalus eucnemis, Gymnocanthus galeatus, Halocynthia aurantium, Hemilepidotus jordani, Hemitripterus bolini, Hexagrammos decagrammus, Hippasteria phrygiana, Hippoglossoides elassodon, Hippoglossus stenolepis, Isopsetta isolepis, Labidochirus splendescens, Leuroglossus schmidti, Limanda aspera, Lopholithodes foraminatus, Lumpenella longirostris, Lycodes brevipes, Lycodes diapterus, Lycodes palearis, Lyopsetta exilis, Malacocottus zonurus, Mallotus villosus, Mesocentrotus franciscanus, Microgadus proximus, Microstomus pacificus, Modiolus modiolus, Myoxocephalus jaok, Myoxocephalus polyacanthocephalus, Neptunea lyrata, Neptunea pribiloffensis, Oncorhynchus keta, Oncorhynchus tshawytscha, Ophiodon elongatus, Oregonia gracilis, Pagurus aleuticus, Pagurus brandti, Pagurus ochotensis, Pandalopsis dispar, Pandalus eous, Pandalus jordani, Parophrys vetulus, Pasiphaea pacifica, Patinopecten caurinus, Platichthys stellatus, Pleurogrammus monopterygius, Pleuronectes quadrituberculatus, Podothecus accipenserinus, Psettichthys melanostictus, Pycnopodia helianthoides, Raja binoculata, Raja rhina, Rhinolithodes wosnessenskii, Sebastes alutus, Sebastes babcocki, Sebastes borealis, Sebastes polyspinis, Sebastes ruberrimus, Sebastes variegatus, Sebastes zacentrus, Sebastolobus alascanus, Somniosus pacificus, Squalus acanthias, Strongylocentrotus droebachiensis, Strongylocentrotus fragilis, Strongylocentrotus pallidus, Stylasterias forreri, Thaleichthys pacificus, Theragra chalcogramma, Trichodon trichodon, Triglops forficatus, Triglops scepticus, Zaprora silenus

neus

Acipenser oxyrinchus, Alosa aestivalis, Alosa pseudoharengus, Alosa sapidissima, Amblyraja radiata, Ammodytes dubius, Anarhichas lupus, Anchoa hepsetus, Anchoa mitchilli, Antigonia capros, Argentina silus, Argentina striata, Aspidophoroides monopterygius, Atlantopandalus propinqvus, Bairdiella chrysoura, Bathynectes longispina, Bathypolypus arcticus, Brevoortia tyrannus, Brosme brosme, Cancer borealis, Cancer plebejus, Carcharhinus plumbeus, Centropristis philadelphica, Centropristis striata, Chaceon quinquedens, Chionoecetes opilio, Chlorophthalmus agassizi, Citharichthys arctifrons, Clupea harengus, Conger oceanicus, Crangon septemspinosa, Cryptacanthodes maculatus, Cyclopterus lumpus, Cynoscion regalis, Dasyatis centroura, Dasyatis say, Decapterus punctatus, Dichelopandalus leptocerus, Dipturus laevis, Enchelyopus cimbrius, Etropus microstomus, Etrumeus teres(sadina), Foetorepus agassizii, Gadus morhua, Glyptocephalus cynoglossus, Gymnura altavela, Helicolenus dactylopterus, Hemitripterus americanus, Hippoglossina oblonga, Hippoglossoides platessoides, Hippoglossus hippoglossus, Homarus americanus, Illex illecebrosus, Lagodon rhomboides, Larimus fasciatus, Lebbeus polaris, Leiostomus xanthurus, Lepophidium profundorum, Leptoclinus maculatus, Leucoraja erinacea, Leucoraja garmani, Leucoraja ocellata, Limanda ferruginea, Limulus polyphemus, Liparis atlanticus, Lithodes maja, Loligo pealeii, Lolliguncula brevis, Lophius americanus, Lopholatilus chamaeleonticeps, Lumpenus lampretaeformis, Lycenchelys verrillii, Macrorhamphosus scolopax, Malacoraja senta, Maurolicus weitzmani, Melanogrammus aeglefinus, Melanostigma atlanticum, Menidia menidia, Menticirrhus americanus, Menticirrhus saxatilis, Merluccius albidus, Merluccius bilinearis, Micropogonias undulatus, Monolene sessilicauda, Morone saxatilis, Mustelus canis, Myliobatis freminvillii, Myoxocephalus aenaeus, Myoxocephalus octodecemspinosus, Myxine glutinosa, Nemichthys scolopaceus, Ophidion marginatum, Osmerus mordax, Ovalipes ocellatus, Ovalipes stephensoni, Pandalus borealis, Pandalus montagui, Paralichthys dentatus, Parasudis truculenta, Pasiphaea multidentata, Peprilus triacanthus, Peristedion miniatum, Petromyzon marinus, Phycis chesteri, Placopecten magellanicus, Pollachius virens, Polymixia lowei, Pomatomus saltatrix, Pontinus longispinis, Pontophilus norvegicus, Prionotus alatus, Prionotus carolinus, Prionotus evolans, Pseudopleuronectes americanus, Raja eglanteria, Scomber scombrus, Scophthalmus aquosus, Scyliorhinus retifer, Sebastes fasciatus, Sicyonia brevirostris, Squalus acanthias, Squatina dumeril, Stenotomus chrysops, Syacium papillosum, Symphurus plagiusa, Synagrops bellus, Syngnathus fuscus, Synodus foetens, Synodus poeyi, Tautogolabrus adspersus, Trachinocephalus myops, Trachurus lathami, Trichiurus lepturus, Triglops murrayi, Trinectes maculatus, Ulvaria subbifurcata, Urophycis chuss, Urophycis regia, Urophycis tenuis, Zenopsis conchifera, Zoarces americanus

newf

Alepocephalus bairdii, Amblyraja jenseni, Amblyraja radiata, Ammodytes dubius, Anarhichas denticulatus, Anarhichas lupus, Arctogadus glacialis, Arctozenus risso kroyeri, Argentina silus, Artediellus atlanticus, Artediellus uncinatus, Aspidophoroides olrikii, Bathylagus euryops, Bathyraja richardsoni, Centroscyllium fabricii, Ceramaster granularis, Chiasmodon niger, Chionoecetes opilio, Coryphaenoides guentheri, Cottunculus thomsonii, Crossaster papposus, Eualus gaimardii gaimardii, Eualus pusiolus, Eumicrotremus spinosus, Flabellum macandrewi, Gersemia rubiformis, Glyptocephalus cynoglossus, Gymnelus viridis, Hemitripterus americanus, Hippoglossoides platessoides, Hyas araneus, Icelus bicornis, Illex coindetii, Lebbeus groenlandicus, Leptagonus decagonus, Limanda ferruginea, Liparis atlanticus, Lumpenus fabricii, Lumpenus lampretaeformis, Lycodes lavalaei, Lycodes reticulatus, Malacoraja senta, Mallotus villosus, Merluccius albidus, Micromesistius poutassou, Myoxocephalus aenaeus, Myoxocephalus scorpioides, Myoxocephalus scorpius, Myxine glutinosa, Nemichthys scolopaceus, Notacanthus chemnitzii, Ophiura robusta, Pandalus borealis, Pandalus montagui, Paragorgia arborea, Pasiphaea princeps, Pasiphaea tarda, Pollachius virens, Polyacanthonotus rissoanus, Poromitra capito, Primnoa resedaeformis, Sabinea sarsii, Sabinea septemcarinata, Sebastes norvegicus, Sergestes arcticus, Serrivomer beanii, Spirontocaris phippsii, Stichaeus punctatus, Synaphobranchus kaupii, Triglops murrayi, Trisopterus esmarkii, Urophycis regia

sa

Acanthostracion quadricornis, Achelous spinimanus, Alectis ciliaris, Aluterus schoepfii, Ancylopsetta ommata, Arenaeus cribrarius, Ariopsis felis, Bagre marinus, Bairdiella chrysoura, Brevoortia tyrannus, Calamus leucosteus, Calappa flammea, Callinectes ornatus, Callinectes sapidus, Callinectes similis, Caranx crysos, Carcharhinus acronotus, Carcharhinus limbatus, Caretta caretta, Centropristis philadelphica, Centropristis striata, Chaetodipterus faber, Chilomycterus schoepfii, Chloroscombrus chrysurus, Citharichthys macrops, Citharichthys spilopterus, Cynoscion nothus, Cynoscion regalis, Dasyatis americana, Dasyatis say, Decapterus punctatus, Diplectrum formosum, Dyspanopeus sayi, Echeneis naucrates, Etropus crossotus, Etropus cyclosquamus, Etrumeus teres(sadina), Farfantepenaeus aztecus, Farfantepenaeus duorarum, Gibbesia neglecta, Gymnura micrura, Haemulon aurolineatum, Harengula jaguana, Hepatus epheliticus, Hippocampus erectus, Hypleurochilus geminatus, Lagodon rhomboides, Larimus fasciatus, Leiostomus xanthurus, Litopenaeus setiferus, Lolliguncula brevis, Menippe mercenaria, Menticirrhus americanus, Menticirrhus littoralis, Menticirrhus saxatilis, Micropogonias undulatus, Mobula hypostoma, Mustelus canis, Myliobatis freminvillii, Opisthonema oglinum, Orthopristis chrysoptera, Ovalipes ocellatus, Ovalipes stephensoni, Pagurus pollicaris, Paralichthys albigutta, Paralichthys dentatus, Paralichthys lethostigma, Paralichthys squamilentus, Peprilus paru, Peprilus triacanthus, Persephona mediterranea, Pilumnus sayi, Pomatomus saltatrix, Portunus gibbesii, Prionotus carolinus, Prionotus evolans, Prionotus rubio, Prionotus scitulus, Prionotus tribulus, Rachycentron canadum, Raja eglanteria, Rhinobatos lentiginosus, Rhinoptera bonasus, Rhizoprionodon terraenovae, Sardinella aurita, Scomberomorus cavalla, Scomberomorus maculatus, Scophthalmus aquosus, Selene setapinnis, Selene vomer, Sphoeroides maculatus, Sphyraena guachancho, Sphyrna lewini, Sphyrna tiburo, Squilla empusa, Stellifer lanceolatus, Stephanolepis hispidus, Syacium papillosum, Symphurus plagiusa, Synodus foetens, Trachinotus carolinus, Trichiurus lepturus, Trinectes maculatus, Xiphopenaeus kroyeri

shelf

Alosa pseudoharengus, Alosa sapidissima, Amblyraja radiata, Ammodytes dubius, Anarhichas lupus, Arctozenus risso, Argentina silus, Artediellus atlanticus, Artediellus uncinatus, Aspidophoroides monopterygius, Brosme brosme, Citharichthys arctifrons, Clupea harengus, Cyclopterus lumpus, Enchelyopus cimbrius, Eumicrotremus spinosus, Gadus morhua, Glyptocephalus cynoglossus, Helicolenus dactylopterus, Hemitripterus americanus, Hippoglossoides platessoides, Hippoglossus hippoglossus, Leptagonus decagonus, Leptoclinus maculatus, Leucoraja erinacea, Leucoraja ocellata, Limanda ferruginea, Lophius americanus, Lumpenus lampretaeformis, Lycodes vahlii, Malacoraja senta, Mallotus villosus, Melanogrammus aeglefinus, Merluccius bilinearis, Myoxocephalus octodecemspinosus, Myxine glutinosa, Nezumia bairdii, Peprilus triacanthus, Phycis chesteri, Pollachius virens, Pseudopleuronectes americanus, Reinhardtius hippoglossoides, Scomber scombrus, Squalus acanthias, Triglops murrayi, Urophycis chuss, Urophycis tenuis, Zoarces americanus

wctri

Allosmerus elongatus, Alosa sapidissima, Anoplopoma fimbria, Apristurus brunneus, Argentina sialis, Atheresthes stomias, Bathyagonus pentacanthus, Bathyraja interrupta, Chilara taylori, Citharichthys sordidus, Clupea pallasii pallasii, Cymatogaster aggregata, Engraulis mordax, Enteroctopus dofleini, Eopsetta jordani, Gadus macrocephalus, Genyonemus lineatus, Glyptocephalus zachirus, Gorgonocephalus eucnemis, Hexagrammos decagrammus, Hippasteria phrygiana, Hippoglossoides elassodon, Hippoglossus stenolepis, Hydrolagus colliei, Icelinus filamentosus, Isopsetta isolepis, Loligo opalescens, Lopholithodes foraminatus, Luidia foliolata, Lycodes cortezianus, Lycodes diapterus, Lycodes pacificus, Lyopsetta exilis, Mediaster aequalis, Merluccius productus, Metacarcinus magister, Metridium dianthus, Microgadus proximus, Microstomus pacificus, Oncorhynchus tshawytscha, Ophiodon elongatus, Pandalopsis dispar, Pandalus eous, Pandalus jordani, Pandalus platyceros, Parophrys vetulus, Peprilus simillimus, Pisaster brevispinus, Platichthys stellatus, Pleurobranchaea californica, Pleuronichthys decurrens, Pleuronichthys verticalis, Porichthys notatus, Psettichthys melanostictus, Pycnopodia helianthoides, Raja binoculata, Raja inornata, Raja rhina, Rathbunaster californicus, Rossia pacifica, Scomber japonicus, Sebastes alutus, Sebastes babcocki, Sebastes brevispinis, Sebastes chlorostictus, Sebastes crameri, Sebastes diploproa, Sebastes elongatus, Sebastes entomelas, Sebastes flavidus, Sebastes goodei, Sebastes helvomaculatus, Sebastes jordani, Sebastes paucispinis, Sebastes pinniger, Sebastes proriger, Sebastes reedi, Sebastes ruberrimus, Sebastes saxicola, Sebastes semicinctus, Sebastes wilsoni, Sebastes zacentrus, Sebastolobus alascanus, Squalus acanthias, Strongylocentrotus fragilis, Thaleichthys pacificus, Theragra chalcogramma, Torpedo californica, Trachurus symmetricus, Xeneretmus latifrons, Zalembius rosaceus, Zaniolepis latipinnis Empty data.table (0 rows) of 1 col: reg

Figure S2. MSOM - naive scatter

naive_msom_scatter()
**Figure S1.** MSOM richness vs naive richness

Figure S1. MSOM richness vs naive richness

MSOM richness and Naive richness are pretty similar. MSOM richness is probably more accurate, or is at least more conservative b/c it has fewer significant trends. But their similarity should help justify using observed presences/ absences in other analyses.

Manuscript paragraph:
MSOM estimates of richness were greater than Naive estimates, but the two methods produced similar temporal dynamics in richness (Figure S1). Henceforth, we report MSOM richness estimates. The greatest long-term average richness was the Gulf of Mexico (142.3), lowest in the Scotian Shelf (46.3). The inter-region average of long-term standard deviations of richness was 5.3; the Aleutian Islands showed the lowest variability (sd = 2.4), and the Gulf of Alaska was the most variable (sd = 8.5).

ur <- comm_master[,unique(reg)]
nr <- length(ur)
naive_msom_mod <- list()
for(r in 1:nr){
    td <- comm_master[reg==ur[r]]
    naive_msom_mod[[ur[r]]] <- lm(reg_rich~naive_rich, data=td)
}

diff1 <- function(x){
    co <- summary(x)$coeff
    est <- co["naive_rich","Estimate"]
    se <- co["naive_rich","Std. Error"]
    # est + sign(est)*1.96*se
    
    pnorm(1-est, sd=se, lower.tail=FALSE)
}
rbindlist(lapply(naive_msom_mod, mod_smry, pred_name="naive_rich"), idcol='reg')
##      reg Class              mod_call  predictor estimate p.value Marginal
## 1:    ai    lm reg_rich ~ naive_rich naive_rich  0.76768   0e+00   0.9094
## 2:   ebs    lm reg_rich ~ naive_rich naive_rich  0.85367   0e+00   0.9799
## 3:  gmex    lm reg_rich ~ naive_rich naive_rich  0.70116   0e+00   0.8240
## 4:   goa    lm reg_rich ~ naive_rich naive_rich  0.76002   2e-04   0.7283
## 5:  neus    lm reg_rich ~ naive_rich naive_rich  1.04916   0e+00   0.8834
## 6:  newf    lm reg_rich ~ naive_rich naive_rich  1.06926   0e+00   0.9917
## 7:    sa    lm reg_rich ~ naive_rich naive_rich  0.83276   1e-03   0.3797
## 8: shelf    lm reg_rich ~ naive_rich naive_rich  0.74526   0e+00   0.9006
## 9: wctri    lm reg_rich ~ naive_rich naive_rich  0.97977   0e+00   0.9914
##    Conditional     AIC
## 1:          NA  30.333
## 2:          NA  78.322
## 3:          NA  73.003
## 4:          NA  80.570
## 5:          NA 161.988
## 6:          NA  20.860
## 7:          NA 133.744
## 8:          NA 123.260
## 9:          NA  25.122
sapply(naive_msom_mod, diff1)
##         ai        ebs       gmex        goa       neus       newf 
## 1.2144e-03 5.9555e-11 1.7715e-04 4.3195e-02 7.6001e-01 9.9597e-01 
##         sa      shelf      wctri 
## 2.2556e-01 6.5869e-11 2.6534e-01

All regions except Northeast U.S. and Newfoundland have estimates that are less than 1, although West Coast U.S. is not signifiantly less than 1. Therefore, for two-thirds of the regions, the MSOM tended to estimate that more undetected species were present when naive estimates were low.

Table S1. Summary of Sampling in Each Region

sumry_counts <- data_all[reg!="wcann", 
    j = {
        yi <- table(diff(sort(unique(year))))
        yi_form <- paste0(names(yi), paste("(",yi,")",sep=""))
        data.table(
            "N" = trawlData::lu(year),
            "Years" = paste(min(year),max(year),sep=" - "),
            "Frequency" = paste(yi_form,collapse=", "),
            "Sites" = trawlData::lu(stratum), 
            "Tows" = paste0(
                .SD[,trawlData::lu(haulid),by=c("stratum","year")][,max(V1)],
                paste0("(",.SD[,trawlData::lu(haulid),by=c("stratum","year")][,round(mean(V1),1)],")")
                ),
            "Species" = trawlData::lu(spp)
        )
    }, 
    by=c('reg')
]
setnames(sumry_counts, 'reg', "Region")
sumry_counts[,Region:=factor(Region, levels=c("ebs","ai","goa","wctri","gmex","sa","neus","shelf","newf"), labels=c("E. Bering Sea","Aleutian Islands","Gulf of Alaska","West Coast US","Gulf of Mexico","Southeast US", "Northeast US", "Scotian Shelf","Newfoundland"))]
setkey(sumry_counts, Region)

sumry_counts[,Org:=c("AFSC","AFSC","AFSC","NMFS","GSMFC","SCDNR","NEFSC","DFO","DFO")]
stargazer(sumry_counts, summary=FALSE, rownames=FALSE, column.sep.width="2pt", digits.extra=0, digits=NA)
% Table created by stargazer v.5.2 by Marek Hlavac, Harvard University. E-mail: hlavac at fas.harvard.edu % Date and time: Wed, Jun 28, 2017 - 15:54:04 
# \begin{table}[!htbp] \centering
# %  \caption{}
# %  \label{}
# \begin{tabular}{@{\extracolsep{2pt}} cccccccc}
# \\[-1.8ex]\hline
# \hline \\[-1.8ex]
# Region & N & Years & Frequency & Sites & Tows & Species & Org \\
# \hline \\[-1.8ex]
# E. Bering Sea & $31$ & 1984 - 2014 & 1(30) & $138$ & 4(1.6) & $110$ & $\text{AFSC}^{*}$ \\
# Aleutian Islands & $12$ & 1983 - 2014 & 2(5), 3(4), 4(1), 5(1) & $82$ & 12(2.8) & $54$ & $\text{AFSC}^{*}$ \\
# Gulf of Alaska & $13$ & 1984 - 2013 & 2(7), 3(5) & $89$ & 15(4.4) & $98$ & $\text{AFSC}^{*}$ \\
# West Coast US & $10$ & 1977 - 2004 & 3(9) & $84$ & 91(4.7) & $92$ & $\text{NMFS}^{\dagger}$ \\
# Gulf of Mexico & $17$ & 1984 - 2000 & 1(16) & $39$ & 39(5.7) & $144$ & $\text{GSMFC}^{\ddagger}$ \\
# Southeast US & $25$ & 1990 - 2014 & 1(24) & $24$ & 13(3.9) & $104$ & $\text{SCDNR}^{\S}$ \\
# Northeast US & $32$ & 1982 - 2013 & 1(31) & $100$ & 10(3) & $141$ & $\text{NEFSC}^{\P}$ \\
# Scotian Shelf & $41$ & 1970 - 2010 & 1(40) & $48$ & 11(2.5) & $48$ &$\text{DFO}^{\nabla}$ \\
# Newfoundland & $16$ & 1996 - 2011 & 1(15) & $191$ & 9(2.2) & $72$ & $\text{DFO}^{\nabla}$ \\
# \hline \\[-1.8ex]
# \end{tabular}
# \end{table}

# knitr::kable(sumry_counts, caption="Years = Total number of years sampled, Year Range = the minimum and maximum of years sampled, Year Interval = the number of years elapsed between samples (and the frequency of this interval in parentheses), Sites = the total number of sites in the region, Max. Tows = maximum number of tows per site per year, Average Tows = the average number of tows per site per year, Total Species = the total number of species observed in the region across all sites and years.")

Table S2. Naive tau

Table S1. Naive richness trends in each region. Estimate is Kendall’s Tau_b, BH is the Benjamini-Hochberg corrected p-value, and p.value is the original p-value.
reg estimate BH pvalue
ai -0.09091 0.73170 0.73170
ebs 0.50108 0.00018 0.00008
gmex 0.85294 0.00001 0.00000
goa 0.20513 0.40514 0.36012
neus 0.33681 0.01032 0.00803
newf 0.78658 0.00011 0.00004
sa -0.56854 0.00028 0.00016
shelf 0.70488 0.00000 0.00000
wctri 0.76409 0.00456 0.00304

Figure S2. Barplot of categories

# par(cex=1, mar=c(3,1,1,0), ps=8, mgp=c(1,0.25,0), tcl=-0.15, lheight=0.7)
categ_barplot()
# png("~/Desktop/bp.png", width=3.5, height=3.5, res=200, units='in'); categ_barplot(); dev.off()
**Figure S2.** Number of species beloning to the categories of both, neither, colonizer, leaver in each region

Figure S2. Number of species beloning to the categories of both, neither, colonizer, leaver in each region

Number of species in each category in each region.
ai ebs gmex goa neus newf sa shelf wctri
neither 39 64 105 63 56 49 69 27 64
both 6 44 31 17 83 12 35 20 15
colonizer 8 2 8 18 1 10 0 1 12
leaver 1 0 0 0 1 1 0 0 1

It’s the same pattern, whichever way you split it. However, AI is the only region that had more colonizers than both species. An interesting way to think about some of this is that the average sd in richness was 5.29901, so when the number of colonizer or leaver species exceed’s that region’s sd, the impact of those categories, which I consider to be dubious, might start being relevant (though it’s not necessarily problematic, nor is this even close to an actual test for the significance of those categories to the trend). EBS and Shelf had significant positive trends in richness and very low numbers in the colonizer category. WCTRI and NEWF had similar numbers in the both and colonizer category.

Table S3. Attributing Richness Change to Colonizers (only)

Region Richness Change colonizer
E. Bering Sea 12.4666 2
Aleutian Islands 4.2513 8
Gulf of Alaska 9.5026 1
West Coast US 7.3750 8
Gulf of Mexico -5.0019 0
Southeast US 18.8206 12
Northeast US 12.7363 10
Scotian Shelf 7.5842 1
Newfoundland 17.5343 18 
stargazer(att_categ_print, summary=FALSE, rownames=FALSE, column.sep.width="2pt", digits=1, digits.extra=0) # print table
% Table created by stargazer v.5.2 by Marek Hlavac, Harvard University. E-mail: hlavac at fas.harvard.edu % Date and time: Wed, Jun 28, 2017 - 15:54:05 
# \begin{table}[!htbp] \centering
#   %\caption{}
#   %\label{}
# \begin{tabular}{@{\extracolsep{2pt}} ccc}
# \\[-1.8ex]\hline
# \hline \\[-1.8ex]
# Region & Richness Change & Colonizing Species \\
# \hline \\[-1.8ex]
# E. Bering Sea & $12.5$ & $2$ \\
# Aleutian Islands & $4.3$ & $8$ \\
# Gulf of Alaska & $17.5$ & $18$ \\
# West Coast US & $18.8$ & $12$ \\
# Gulf of Mexico & $7.4$ & $8$ \\
# Southeast US & $$-$5.0$ & $0$ \\
# Northeast US & $9.5$ & $1$ \\
# Scotian Shelf & $7.6$ & $1$ \\
# Newfoundland & $12.7$ & $10$ \\
# \hline \\[-1.8ex]
# \end{tabular}
# \end{table}

Figure S4. Total Colonizations/ Extinctions vs Georaphic Range

ceEventRange("mean_size")
**Figure S7.** Number of colonizations and extinctions as a function of range size and range density.

Figure S7. Number of colonizations and extinctions as a function of range size and range density.

Yup, this is definitely a thing. Long-term average range size and range density predict how many colonizations and extinctions a species is likely to have. This will lead nicely into examing how range changes prior to an extinction or after a colonization.

Figure S5. Range Size Absence Time Detailed

par(mfrow=c(3,3), mgp=c(0.85,0.2,0), ps=8, cex=1, mar=c(1.75,1.5,0.75,0.5), oma=c(0.5,0.5,0.1,0.1), tcl=-0.15)
ur <- names(pretty_reg)
for(r in 1:length(ur)){
    t_reg <- ur[r]
    t_dat <- rangeTimeDT[reg==t_reg]
    t_dat[,spp:=paste0(spp,event)]
    t_dat[type=="pre_ext", c("spp","time"):=list(spp=paste0(spp,type),time=-time)]
    setkey(t_dat, spp, type, time)
    scatterLine(t_dat, x="time", y="size", lineBy="spp", colBy=adjustcolor(pretty_col[t_reg], 1), lwdBy=0.5, type='p', xlab="", ylab="")
    if(t_reg=="ai"){
        t_dat[time <=-10,lines(time, size, col='black')]
    }
    t_dat[,points(mean(time), mean(size), pch=19, col='black', cex=1.2),by=c('time')]
    t_dat[,points(mean(time), mean(size), bg=pretty_col[t_reg], pch=21, col='white'),by=c('time')]

    mtext(pretty_reg[t_reg], line=0, side=3, adj=0.1, font=2)
}
mtext("Time to Event", side=1, line=-0.5, outer=TRUE)
mtext("Range Size", side=2, line=-0.5, outer=TRUE)

Extra Stuff (not main text, not supplement)

Figure. Time series of colonizations and extinctions

col_ext_ts()
**Figure NotIncluded.** Number of colonizations (blue) and extinctions (red) over time in each region.

Figure NotIncluded. Number of colonizations (blue) and extinctions (red) over time in each region.

In most regions the differences in colonization and extinction numbers are similar over time. The most obvious exceptions are for the 3 regions that showed large initial spikes in richness; the GOA, GMEX, and AI regions initially have much larger numbers of colonizers than leavers, but this number shrinks rapidly until the two rates are ~equal.

For the regions with significant positive slopes, there is no visually obvious increase in colonizations relative to extinctions over time. Because the colonization and extinction numbers tend to track each other over the long-term, it it would be difficult to attribute the long-term changes in richness to a change in just colonization or extinction rates.

Manuscript paragraph:
A time series of richness can be decomposed into the colonizations and extinctions of individual species over time. We categorized species according to the following colonization extinction patterns: present in all years = neither (536 species), colonized and went extinct = both (263 species), initially absent but present every year after its colonization = colonizer (61 species), initially present but absent every year after its extinction = leaver (4 species). Most regions had the same overall ranking (neither > both > colonizer > leaver), except in the Northeast US where both was the most common and neither second, and in the Aleutian Islands where colonizer was the second most common and both third (Figure S2). In general, changes in richness were not due to permanent departures or introductions of species to the region. Furthermore, colonization and extinction rates did not become more dissimilar over time for any region (Figure NotIncluded). Colonizations were initially greater than extinctions in Aleutian Islands, Gulf of Alaska, and Gulf of Mexico, but this difference disappeared in the latter portion of these time series, as evidenced by these regions’ initially rapid increase in richness that later plateaued. The other regions did not show strong trends in the difference between colonizations and extinctions over time, making it difficult to attribute the long-term trends in richness to changes in just colonization or just extinction rates.

Figure. Changes in Geographic Density before Extinction and after Colonization

rangeSize_absenceTime("rangeDensity")
**Figure 4b.** Geographic range density vs years until extinction (A) and years after colonization (B). For visualization purposes, range density is averaged across species for each unique value on each axis, and a linear model fit through this average. Statistics in main text use unaggregated data. The horizontal axes were formulated as time until (since) the nearest upcoming (previous) absence. Because range density must be zero when either horizontal axis has a value of zero, points at (0,0) were excluded from figures and analyses.

Figure 4b. Geographic range density vs years until extinction (A) and years after colonization (B). For visualization purposes, range density is averaged across species for each unique value on each axis, and a linear model fit through this average. Statistics in main text use unaggregated data. The horizontal axes were formulated as time until (since) the nearest upcoming (previous) absence. Because range density must be zero when either horizontal axis has a value of zero, points at (0,0) were excluded from figures and analyses.

Figure. Novel Colonizations Per Year

fp <- spp_master[present==1,.SD[which.min((year))] ,by=c('reg','spp')]
fp2 <- fp[,list(new_col=sum(col)),keyby=c('reg','year')]
ry_skele <- unique(spp_master[,list(reg,year)])
fp3 <- merge(ry_skele, fp2, all=TRUE, by=c('reg','year'))
fp3[is.na(new_col), new_col:=0]
par(mfrow=c(3,3))
fp3[,plot(year, new_col, type='o', main=reg[1]),by=c('reg')]

Empty data.table (0 rows) of 1 col: reg

Reveals similar information as the number of colonizations per year, except it isolates the number of colonizations by species that have never been seen in the region before. This is the rate at which new species are introduced to the region. An important caveat here is that the trends here are probably biased downward because we onlly included species that were observed in at leat 10 year-sites in order to avoid the inclusion of ultra-rare species. These exclusions reduce the odds that species that colonized a limited number of sites towards the end of the time series met the threshold of 10, especially for regions with relatively few strata.

E.g., say that a species colonized Southeast U.S., which has 24 sites, in the last year of sampling — for this species to be included, it would have had to occupy 42% of the region (10 sites) in its first year present. Across all regions, the average colonizing species occupies only 5% of strata in its first year, and for the 3 species that colonized the Southeast U.S., they colonized only 4.2% of sites, a full order of magnitude lower than what was needed. Depending on the expansion rate, a species would need to first colonize several years before the end of the time series to be included. It’s also worth noting that no region has a new colonizing species towards the end of the time series — this makes a similar point.

Because of the way we eliminated species from our data set, our analysis was extremely conservative with regard to detecting changes in richness, particularly if those changes were going to be the result of changes in the rate of novel introductions (right now I’m a little less clear on what sources of species declines might be affected, other than to say that generally fewer species would have been included due to only being present at the beginning [affects declines more] or end [affects increases more] of the time series). Regions with short time series and few sites were especially prone to having muted changes in richness.

Figure. Relationship between range size and range density

rangeSizeDens()
**Figure S6**. Range density versus range size. In panel A each point is a species-region-year combination. In panel B, each point is a region-year. Range size is the proportion of sites occupied, range density the tows in occupied sites. The community metrics in B is calculated by take each species' long-term average from A, then taking the average across all species present in the community in a given year. Fitted lines in A are from a loess fit.

Figure S6. Range density versus range size. In panel A each point is a species-region-year combination. In panel B, each point is a region-year. Range size is the proportion of sites occupied, range density the tows in occupied sites. The community metrics in B is calculated by take each species’ long-term average from A, then taking the average across all species present in the community in a given year. Fitted lines in A are from a loess fit.

First posterity, I’ll show a figure relating range size and range density. Then I’ll present the figure of how size can ‘predict’ richness. Finally, I’ll explore models more formally expressing the relationship between richness and size.

These plots show that there is a strong relationship between range size and range density. Interestingly, in Figure S6B, the cross-region relationship is negative (if each color had 1 pt), whereas the within-region relationship is positive.

The positive relationship between size and density is not surprising. My interpretation of density is ~population size. Often population size is correlated with range size. I think this is a standard result, but I need to double-check.
##Figure. Range size vs absence time as individual regressions

rangeTimeDT[,nTime:=length(time),by=c("reg","type","event","spp")]
o <- rangeTimeDT[nTime>=3,j={
    getEPR(lm(size~time))
    } ,by=c("reg","type","event","nTime","spp")
]
rangeTime_signif <- o[,list(propSignificant=(sum(Pr<0.05)/sum(!is.na(Pr))),n=sum(!is.na(Pr))),by=c("reg","type")]

# histograms of estimates, p-value, and r-squared split by pre-extinction and post-colonization
par(mfrow=c(4,2), mar=c(2,2,0.5,0.5), cex=1, ps=10, mgp=c(1,0.1,0), tcl=-0.1)
o[,j={hist(Estimate, main=type[1]);NULL},by='type']

Empty data.table (0 rows) of 1 col: type

o[,j={hist(Pr, main=type[1]);NULL},by='type']

Empty data.table (0 rows) of 1 col: type

o[,j={hist(Rsquared, main=type[1]);NULL},by='type']

Empty data.table (0 rows) of 1 col: type

# p value vs number of years in series
setorder(o, nTime)
# o[,j={plot(nTime,Pr); lines(spline(Pr~nTime),col='red',lwd=2)}]
# abline(h=0.05, lwd=1.5)
# abline(h=0.05, col='white', lwd=0.5)
o[,mean(Pr),by='nTime'][,plot(nTime, V1)];

NULL

abline(h=0.05, col='blue', lty=2)

# slope vs number of years in series
# o[,j={plot(nTime,Estimate); lines(spline(Estimate~nTime),col='red',lwd=2)}]
# abline(h=0, lwd=1.5)
# abline(h=0, col='white', lwd=0.5)
o[,mean(Rsquared),by='nTime'][,plot(nTime, V1)];
NULL
**Exploration Figure** histograms of separate regressions of size ~ time; this is for each run-up to an extinction and reach follow-up to a colonization. Trying to understand how regularly the pattern might be observed. Hard to answer because adjusting the restriction on number of events in the run-up or follow-up (nTime) greatly affects the proportion that are significant.

Exploration Figure histograms of separate regressions of size ~ time; this is for each run-up to an extinction and reach follow-up to a colonization. Trying to understand how regularly the pattern might be observed. Hard to answer because adjusting the restriction on number of events in the run-up or follow-up (nTime) greatly affects the proportion that are significant.

Significant trends in range size before ext/ after col. Sample size is number of ‘stretches’.
reg type propSignificant n
ai post_col 0.35714 14
ai pre_ext 0.00000 2
ebs pre_ext 0.27027 37
ebs post_col 0.35294 51
gmex post_col 0.16216 37
gmex pre_ext 0.08333 12
goa post_col 0.25714 35
goa pre_ext 0.25000 4
neus post_col 0.17647 102
neus pre_ext 0.05714 70
newf post_col 0.21053 19
newf pre_ext 0.16667 6
sa pre_ext 0.27027 37
sa post_col 0.08571 35
shelf post_col 0.30769 26
shelf pre_ext 0.06667 15
wctri post_col 0.21739 23
wctri pre_ext 0.50000 2
type proportionSignificant
post_col 0.23635
pre_ext 0.18493

The mixed effect models show a strong tendency for range size to be smaller near an absence. I figured that this relationship wouldn’t be apparent for all cases, which ended up being the result. However, the significance of these relationships depends on the number of years for each event stretch. So sample size matters. On one hand, this could hold implications for the rate of decline, so excluding short stretches might also exclude more cases with abrupt declines/ increases (although, these may well be preceded by long durations of stability, so not all abrupt declines/ increases would be excluded necessarily). However, the slope estimate doesnt change a whole lot across sample size: from 0 to ~10 years, increasing sample size (duration) also increases the slope (going from slightly negative to pretty consistently positive). Then it levels out, and doesn’t continue increasing. So it is not the case that longer stretches are long because they have more gradual slopes, necessarily. Actually, in the range of data for which there does appear to be a trend (0-10 samples), the slope becomes larger which is the opposite of “longer stretches result from more gradual processes” notion (thinking in terms of extinction).

Ultimately, I think the mixed effects model is far more appropriate so long as conclusions are cauched in general patterns, not in being able to detect the pattern for any single species. While it could have been interesting to present the many-regression results too, I think it is a separate analysis to consider how often this rule would apply to individual species. Such an analysis would benefit from understanding when the rule does and does not apply, not just the apparent frequency of relevance.

Figure. Time Series of Local and Regional Richness

localR <- data_all[,list(lR=length(unique(spp))),by=c("reg","stratum","year")]
bothR <- merge(localR, comm_master[,list(reg,year,naive_rich,reg_rich)],by=c("reg","year"))
par(mfrow=c(3,3), cex=1, ps=8, mar=c(2,2,2,2), mgp=c(1,0.2,0), tcl=-0.2)
ureg <- bothR[,unique(reg)]
nreg <- length(ureg)
for(r in 1:nreg){
    comm_master[reg==ureg[r],j={
        plot(year, get(lR), type='l', ylab=lR)
        mtext(reg[1], side=3, line=0, adj=0.1, font=2)
        par(new=TRUE)
        plot(year, get(rR), type='l', col='red', xaxt='n', yaxt='n', xlab='',ylab='')
        axis(side=4, col='red')
        mtext(rR, side=4, line=1, col='red')
        NULL
    }]
}
mtext("Observed Regional (red) and Mean Local (black) Richness", side=3, line=-0.75, outer=TRUE, font=2)

In general, local richness and regional richness are similar. There are differences, possibly in some cases the regional slope might be significant whereas local would not be (I haven’t checked, though). However, the trends aren’t in opposite directions at the two scales.

Comparisons of Alpha, Beta, Gamma Diversity

Figure. Alpha, beta, and gamma diversity (Naive)

eval(figure_setup())
par(mfrow=c(3,1), mar=c(1.75,1.5,0.25,0.25),mgp=c(0.85,0.1,0), tcl=-0.1, cex=1, ps=8)
ureg <- comm_master[,unique(reg)]
nreg <- length(ureg)
ptCol <- bquote(adjustcolor(pretty_col[reg],0.5))
scatterLine(Data=comm_master, x="naive_rich", y="beta_div_obs", lineBy="reg", col=ptCol, pch=20)
scatterLine(Data=comm_master, x="local_rich_obs", y="beta_div_obs", lineBy="reg", col=ptCol, pch=20)
comm_master[,legend("topright",ncol=2,legend=pretty_reg[una(reg)],text.col=pretty_col[una(reg)], inset=c(-0.01, -0.03), bty='n', x.intersp=0.15, y.intersp=0.65)]
   rect                                             text

1: 32.124 30.318,30.318,30.318,30.318,30.318,45.775, 2: 0.081876 0.39137,0.37885,0.36632,0.35380,0.34128,0.39137, 3: 27.532 30.318,30.318,30.318,30.318,30.318,45.775, 4: 0.40726 0.39137,0.37885,0.36632,0.35380,0.34128,0.39137,

scatterLine(Data=comm_master, x="naive_rich", y="local_rich_obs", lineBy="reg", col=ptCol, pch=20)

Figure. Alpha, beta, and gamma diversity (MSOM)

eval(figure_setup())
par(mfrow=c(3,1), mar=c(1.75,1.5,0.25,0.25),mgp=c(0.85,0.1,0), tcl=-0.1, cex=1, ps=8)
ureg <- comm_master[,unique(reg)]
nreg <- length(ureg)
ptCol <- bquote(adjustcolor(pretty_col[reg],0.5))
scatterLine(Data=comm_master, x="reg_rich", y="beta_div_mu", lineBy="reg", col=ptCol, pch=20)
scatterLine(Data=comm_master, x="local_rich", y="beta_div_mu", lineBy="reg", col=ptCol, pch=20)
comm_master[,legend("topright",ncol=2,legend=pretty_reg[una(reg)],text.col=pretty_col[una(reg)], inset=c(-0.01, -0.03), bty='n', x.intersp=0.15, y.intersp=0.65)]
  rect                                             text

1: 50.059 48.689,48.689,48.689,48.689,48.689,72.775, 2: 0.11305 0.36096,0.34367,0.32638,0.30909,0.29180,0.36096, 3: 44.348 48.689,48.689,48.689,48.689,48.689,72.775, 4: 0.38291 0.36096,0.34367,0.32638,0.30909,0.29180,0.36096,

scatterLine(Data=comm_master, x="reg_rich", y="local_rich", lineBy="reg", col=ptCol, pch=20)

Richness-range size, varying long-term and annual, all spp and transients only

noNeither <- spp_master[,j={
    td <- .SD[ce_categ!="neither" & present==1]
    td1.0 <- td[,list(propStrata_noNeither_ltAvg=mean(range_size_mu)),keyby=c("reg","spp")]
    setkey(td, reg, spp)
    td1.1 <- td[td1.0]
    td1.2 <- td1.1[,list(propStrata_noNeither_avg_ltAvg=mean(propStrata_noNeither_ltAvg)),by=c("reg","year")]
    td2 <- td[,list(propStrata_noNeither_avg=mean(range_size_mu)),by=c("reg","year")]
    td_out <- merge(td1.2, td2, by=c('reg','year'))
}]
cmNN <- merge(comm_master, noNeither)

par(mfrow=c(2,2))
ureg <- comm_master[,unique(reg)]
nreg <- length(ureg)
ptCol <- bquote(adjustcolor(pretty_col[reg],0.5))
scatterLine(Data=cmNN, x="range_size_mu_avg_ltAvg", y="reg_rich", lineBy="reg", col=ptCol, pch=20)
scatterLine(Data=cmNN, x="range_size_mu_avg", y="reg_rich", lineBy="reg", col=ptCol, pch=20)
scatterLine(Data=cmNN, x="propStrata_noNeither_avg_ltAvg", y="reg_rich", lineBy="reg", col=ptCol, pch=20)
scatterLine(Data=cmNN, x="propStrata_noNeither_avg", y="reg_rich", lineBy="reg", col=ptCol, pch=20)

Range Size and Extinction Probability

Statistics for Range Size Year before Extinction

std_range_t1 <- spp_master[ce_categ!='neither' & ce_categ!="colonizer", j={
    
    std_range <- .SD[,list(year, ext, std_range=c((get(rSMet_base))), ext_dist=ext_dist),by=c("spp")]
    setkey(std_range, spp, year)
    std_range_t1 <- std_range[present==1,list(year=year[-1], ext=ext[-1], std_range=std_range[-1], std_range_t1=head(std_range, -1), ext_dist=ext_dist[-1]),by=c("spp")]
    
    std_range_t1[,nspp:=length(unique(spp)),by=c('year')]
    std_range_t1
    
},by="reg"]
# print(std_range_t1[,{print(summary(glm(ext~std_range, family='binomial')));NULL},by='reg'])
# print(std_range_t1[,{print(summary(glmer(ext~std_range+(std_range|reg), family='binomial')));NULL}])

# Set up -- region names and empty named lists
ur <- std_range_t1[,unique(reg)]
rangeExtProb1 <- structure(vector("list",length(ur)), .Names=ur)
rangeExtProb2 <- structure(vector("list",length(ur)), .Names=ur)
rangeExtProb3 <- structure(vector("list",length(ur)), .Names=ur)

# Fit 3 models for each region
for(r in 1:length(ur)){
    t_reg <- ur[r]
    t_dat <- std_range_t1[reg==t_reg]
    rangeExtProb1[[t_reg]] <- (glm(ext~std_range, family='binomial', data=t_dat))
    rangeExtProb2[[t_reg]] <- summary(glm(ext~std_range+nspp, family='binomial', data=t_dat))
    rangeExtProb3[[t_reg]] <- summary(glm(ext~std_range*nspp, family='binomial', data=t_dat))
}
rangeExtProb1_smry <- (smry_modList(rangeExtProb1, pred_name="std_range"))[,reg:=names(rangeExtProb1)]
rangeExtProb1_smry[,BH:=p.adjust(p.value, method='BH')]

Figure for Range Size Year before Extinction

par(mfrow=c(3,3), mar=c(2.5,2.5,1.5,0.5), ps=10, mgp=c(0.75,0.15,0), tcl=-0.15)
for(r in 1:length(ur)){
    std_range_t1[reg==ur[r],plot(std_range, ext)]
    new_r <- std_range_t1[reg==ur[r],sort(std_range)]
    lines(new_r, predict(rangeExtProb1[[ur[r]]], newdata=data.frame(std_range=new_r), type='response'))
    mtext(pretty_reg[ur[r]], side=3, line=0, adj=0.1, font=2)
}

Statistics for Range Size Predicting Years until Extinction

make_timeRange <- function(densName=c("propTow_occ"), sizeName=c("range_size_samp","range_size_mu","propStrata")){
    rangeTimeDT <-  spp_master[stretch_type=="pre_ext" & !is.na(stretch_type) & propStrata!=0]
    rangeTimeDT <- rangeTimeDT[,list(
        reg=reg, 
        event=as.character(event_year), 
        spp=spp, 
        type=as.character(stretch_type),
        time=ext_dist, 
        size=get(sizeName),
        density=get(densName)
    )]
    return(rangeTimeDT)
}

timeRangeDT <- make_timeRange()
ur <- timeRangeDT[,unique(reg)]
sTime_reg_mods_Inv <- structure(vector("list",length(ur)), .Names=ur)
for(r in 1:length(ur)){
    t_reg <- ur[r]
    t_dat <- timeRangeDT[reg==t_reg]
    sTime_reg_mods_Inv[[t_reg]] <- lme4::lmer(time ~ size + (size|spp), data=t_dat)
}
sTime_reg_smry_Inv <- smry_modList2(sTime_reg_mods_Inv)
kable(sTime_reg_smry_Inv)
reg mod_call MargR2 CondR2 AIC pval_size BH_size randGrp Int size
ai time~size+(size|spp) 0.10570 0.2884 173.60 0.09039 0.203 spp 6.7767 13.7420
ebs time~size+(size|spp) 0.19780 0.4588 1773.99 0.00000 0.000 spp 2.5463 29.0803
gmex time~size+(size|spp) 0.00764 0.3658 641.43 0.47281 0.473 spp 2.8071 10.4723
goa time~size+(size|spp) NA NA 179.91 0.19779 0.297 spp 3.5593 53.2009
neus time~size+(size|spp) 0.00505 0.5083 4075.28 0.41940 0.472 spp 3.1922 15.3583
newf time~size+(size|spp) 0.03149 0.4440 351.84 0.16245 0.292 spp 3.5170 8.4463
sa time~size+(size|spp) 0.23210 0.5018 1969.26 0.00000 0.000 spp 3.0907 23.9555
shelf time~size+(size|spp) 0.08943 0.3414 648.72 0.02742 0.082 spp 2.2084 33.8794
wctri time~size+(size|spp) 0.12500 0.7858 153.90 0.26425 0.340 spp 3.6162 49.8260

Beta Div vs CRI

par(mfrow=c(3,3), mar=c(1.85,1.85, 0.5,0.5), mgp=c(0.65, 0.15, 0), oma=c(0.5, 0.5, 0.25, 0.1), tcl=-0.15, ps=8, cex=1)
ur <- names(pretty_reg)[names(pretty_reg)%in%comm_master[,unique(reg)]]
nr <- length(ur)
for(r in 1:nr){
    comm_master[reg==ur[r],j={
        plot(beta_div_obs, propStrata_avg_ltAvg, xlab='', ylab='')
        mod <- lm(propStrata_avg_ltAvg~beta_div_obs)
        abline(mod)
    }]
    mtext(pretty_reg[ur[r]], side=3, adj=0.1, font=2)
}

Boxplot Time Series of Range Size, Color is Richness of Transient Species (Resampled)

eval(figure_setup())
eval(neitherPres_subColor())
boxRange_colRich(range_type="range_size_samp")

Richness Trend vs Transient Range Trend

dat <- merge(transExpansionStats, comm_master[,coef(lm(reg_rich~year))[2], by='reg'], by='reg')
dat[,summary(lm(V1~year))]

Call: lm(formula = V1 ~ year)

Residuals: Min 1Q Median 3Q Max -0.3989 -0.1088 0.0060 0.0928 0.3423

Coefficients: Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.170 0.111 1.53 0.169
year 106.791 38.768 2.75 0.028 * — Signif. codes: 0 ‘’ 0.001 ’’ 0.01 ’’ 0.05 ‘.’ 0.1 ‘’ 1

Residual standard error: 0.238 on 7 degrees of freedom Multiple R-squared: 0.52, Adjusted R-squared: 0.452 F-statistic: 7.59 on 1 and 7 DF, p-value: 0.0283

dat[,plot(year, V1, col=pretty_col[reg], pch=19, xlab="Rate of Range Expansion by Transient Species", ylab="Rate of Change in Species Richness")]

NULL

The significance of this trend depends on Southeast US, though. I’m not sure I want to get into defending a plot based on an outlier, and the fact that I didn’t account for uncertainty in the x-axis.

Sys.time()
## [1] "2017-06-28 15:54:16 EDT"
sessionInfo()
## R version 3.3.0 (2016-05-03)
## Platform: x86_64-apple-darwin13.4.0 (64-bit)
## Running under: OS X 10.11.6 (El Capitan)
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] texreg_1.36.4        stargazer_5.2        kfigr_1.2           
##  [4] xtable_1.8-2         rmarkdown_1.0        knitr_1.14          
##  [7] viridis_0.4.0        viridisLite_0.2.0    piecewiseSEM_1.1.3  
## [10] spdep_0.6-5          spatstat_1.45-2      rpart_4.1-10        
## [13] nlme_3.1-127         raster_2.5-2         sp_1.2-3            
## [16] maps_3.1.0           multcomp_1.4-5       TH.data_1.0-7       
## [19] MASS_7.3-45          survival_2.39-2      mvtnorm_1.0-5       
## [22] car_2.1-2            lme4_1.1-12          Matrix_1.2-6        
## [25] rbLib_0.1.1          trawlDiversity_0.5.0 trawlData_0.4.0     
## [28] data.table_1.10.4   
## 
## loaded via a namespace (and not attached):
##  [1] bit64_0.9-5        splines_3.3.0      gtools_3.5.0      
##  [4] highr_0.6          stats4_3.3.0       yaml_2.1.13       
##  [7] LearnBayes_2.15    pbivnorm_0.6.0     lattice_0.20-33   
## [10] quantreg_5.21      quadprog_1.5-5     digest_0.6.10     
## [13] polyclip_1.5-6     ggm_2.3            minqa_1.2.4       
## [16] colorspace_1.2-6   sandwich_2.3-4     htmltools_0.3.5   
## [19] plyr_1.8.4         SparseM_1.7        gmodels_2.16.2    
## [22] scales_0.4.0       gdata_2.17.0       tensor_1.5        
## [25] MatrixModels_0.4-1 mgcv_1.8-12        ggplot2_2.1.0     
## [28] nnet_7.3-12        pbkrtest_0.4-6     mnormt_1.5-4      
## [31] magrittr_1.5       deldir_0.1-12      evaluate_0.9      
## [34] tools_3.3.0        formatR_1.4        stringr_1.2.0     
## [37] munsell_0.4.3      grid_3.3.0         nloptr_1.0.4      
## [40] goftest_1.0-3      igraph_1.0.1       lavaan_0.5-20     
## [43] boot_1.3-18        gtable_0.2.0       codetools_0.2-14  
## [46] abind_1.4-3        gridExtra_2.2.1    zoo_1.7-13        
## [49] bit_1.1-12         stringi_1.1.5      parallel_3.3.0    
## [52] Rcpp_0.12.10       coda_0.18-1